I noticed today that the very place on your body that you swatted a fly, and killed it, more flies would go to the same spot.
This could be because the scent of the said deceased fly is on your skin, or because your own body, whilst dealing with the pain it's just received, gives off it's own attractive allure.
So, the way forward here is to give your wife a good slapping (all over) before you go out sunbathing, then lie next to her in your own fly free area.
I think this has some merit. Let me know if it works for you.